The invention is related to the field of wireless systems, and in particular to a resonant wireless power system that allows power to be transferred throughout with variations in matching networks efficiently.
In a wireless power system, inductive coils forming a loosely-coupled transformer are used to transfer power in a non-contact fashion. In a resonant wireless power (RWP) system, impedance-matching networks are used to cancel the reactive impedance of those inductive coils, allowing power to be transferred through the system more effectively. In an idealized RWP system with a resistive load, the matching networks can be tuned perfectly to null out all reactive impedance, creating a perfectly matched circuit. In practical RWP systems, however, this idealized model does not hold. Load power varies according to the demands of the device being serviced, resulting in a varying load impedance. The coupling factor between the source and load coils changes with the relative position of the charger and charging device. And, in mass-produced devices, the matching networks suffer from manufacturing variations, so they are never perfectly in tune.
There are two complex impedances that can be used to describe most of the important aspects of a RWP system: the open-circuit impedance Zoc and the reflected impedance Zref. Mutual inductance, or coupling, between the source coil and receiver coil can be modeled in a number of different ways. In our preferred method, the coupling is modeled as a current-controlled voltage source in series with the receiver (secondary) coil. The impedance seen by this voltage source, which includes the coil, matching network and load (rectifier, dc/dc, load current), is Zoc. On the source (primary) side, when coupling is present, one can model the effect of the coupling as an impedance in series with the source coil called Zref, the reflected impedance. Both the open-circuit impedance and the reflected impedance are complex quantities—they have real (resistive) and imaginary (reactive) components. For a 1:1 RWP system, the reflected impedance is related to the open-circuit impedance by this formula:
      Z    ref    =                    (                  ω          ⁢                                          ⁢          M                )            2              Z      oc      